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Formula sheet Test 1

Formula sheet Test 1 - Formula Sheet for Test 1-— you may...

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Unformatted text preview: Formula Sheet for Test 1 -— you may add your own notes to this sheet Cycle Time CTs(M/M/) 1) WIP given throughput A, 0T8, use Littles’ Law WI P3 = ACTS. Imperfect Servers S normal service time and T is imperfect service time a = availability Em = E [31/ a 02[T] = C2[3] + a(1 — a)(1 + 02[R])E[R]/E[S] Expectations E[aX + b] = aE{X] + b ‘V[aX + b] = 2I/[X] +0 V[X] = ElXZ] "- EEK]2 02m = ‘VL’Q/EIX}2 Elk-'2] = (02% + 1)E[X]2 Exponential random variable T w f (t) z Ae‘dt, t 2 0 7 E[T]=1/)\, V[T]=1//\2, C2[T]=1 n A Poisson random variable N N p(t)= Elna—t, t > 0 n _>_ 0 E[N]=A, V[T]=)\, 02[N]=1 Departures Em] m 1/,\ . C2[Td] m Cg = (l — u2)02[Ta] + u202[S], for capacity c = 1 02m] = 03 = 1 + (1 — “2)(02ml "' 1) +u2(02[31 — 1)/\/5, Random Splitting of Departure Streams 0% *‘v k) = PMCW) + (1 - PM) ...
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